INVESTIGATION
Cost of Adaptation and Fitness Effects of Beneficial
Mutations in Pseudomonas fluorescens
Thomas Bataillon,* Tianyi Zhang,† and Rees Kassen†,1
*Bioinformatics Research Center, Aarhus University, 8000C Aarhus, Denmark, and †Center for Advanced Research in
Environmental Genomics, Department of Biology, University of Ottawa, Ottawa K1N 6N5, Canada
ABSTRACT Adaptations are constructed through the sequential substitution of beneficial mutations by natural selection. However, the
rarity of beneficial mutations has precluded efforts to describe even their most basic properties. Do beneficial mutations typically confer
small or large fitness gains? Are their fitness effects environment specific, or are they broadly beneficial across a range of
environments? To answer these questions, we used two subsets (n ¼ 18 and n ¼ 63) of a large library of mutants carrying antibiotic
resistance mutations in the bacterium Pseudomonas fluorescens whose fitness, along with the antibiotic sensitive ancestor, was
assayed across 95 novel environments differing in the carbon source available for growth. We explore patterns of genotype-byenvironment (G·E) interactions and ecological specialization among the 18 mutants initially found superior to the sensitive ancestor
in one environment. We find that G·E is remarkably similar between the two sets of mutants and that beneficial mutants are not
typically associated with large costs of adaptation. Fitness effects among beneficial mutants depart from a strict exponential distribution: they assume a variety of shapes that are often roughly L shaped but always right truncated. Distributions of (beneficial) fitness
effects predicted by a landscape model assuming multiple traits underlying fitness and a single optimum often provide a good
description of the empirical distributions in our data. Simulations of data sets containing a mixture of single and double mutants
under this landscape show that inferences about the distribution of fitness effects of beneficial mutants is quite robust to contamination by second-site mutations.
B
ENEFICIAL mutations provide the raw material for adaptive evolution. Yet little is known about the properties of
beneficial mutations because population genetics theory has
placed far more emphasis on understanding the more abundant class of deleterious mutations (Eyre-Walker and
Keightley 2007). The reason for this derives largely from
arguments for the importance of neutrality in molecular
evolution, which posit that beneficial mutations should be
so rare that they would almost never be seen in nature. The
result is a rich body of theory on the importance of deleterious mutations for the evolution of genetic systems such as
ploidy, recombination, and life cycles. However, the theory
has been comparatively silent on beneficial mutations, the
“stuff” of adaptive evolution (Orr 2005).
Copyright © 2011 by the Genetics Society of America
doi: 10.1534/genetics.111.130468
Manuscript received May 7, 2011; accepted for publication August 10, 2011
Supporting information is available online at http://www.genetics.org/cgi/content/
full/genetics.111.130468/DC1.
1
Corresponding author: University of Ottawa, 30 Marie Curie, P.O. Box 450, Station A,
Ottawa, ON K1N 6N5, Canada. E-mail: [email protected]
The realization that a genuinely predictive theory of
evolution must be able to accommodate all mutations—
whether they be deleterious, neutral, or beneficial—has
led to attempts on both the theoretical and empirical fronts
to describe the distribution of fitness effects (DFE) among
mutations exposed to selection. Although we are still some
way from describing the complete DFE among all mutations,
theoretical work stemming from the mutational landscape
models of Gillespie (1984) suggests that restricting attention to beneficial mutations may provide the beginnings of
a general theory of adaptive evolution (Joyce et al. 2008).
The essential insight here is that, provided the starting genotype is already fairly well adapted to a given set of conditions, beneficial mutations represent draws from the righthand tail of a complete DFE. This fact allows us to use
extreme value theory (EVT) to describe the distribution of
fitness effects among beneficial mutations, even if the complete DFE remains difficult to characterize. The key result is
that, regardless of the underlying probability distributions
used to model the DFE (the exponential, normal, and
gamma distributions are the ones most often employed),
Genetics, Vol. 189, 939–949 November 2011
939
the DFE among beneficial mutations has an exponentially
distributed right tail, with many mutations of small effect
and few of large effect (Orr 2003).
The generality of this prediction can be questioned on at
least four counts. First, the theory concerns the spectrum of
fitness effects among single mutations, meaning those that
are a single nucleotide away from the wild-type sequence.
Double mutants are assumed to be rare and effectively
ignored. However, direct sequencing of whole genomes from
mutation accumulation experiments puts the genome-wide
mutation rate, U, approximately two to three orders of magnitude higher than had previously been estimated from phenotypic analyses (reviewed in Halligan and Keightley 2009).
In yeast, for example, indirect estimates of U average four
mutations in every 1000 genomes replicated, but Lynch
et al. (2008) estimated that U = 0.32 using whole-genome
resequencing. Double mutants may thus be sufficiently common to impact the DFE among mutations, especially in populations of bacteria or viruses with large population sizes.
It is unclear how such contamination of the spectrum of
mutants available to selection affects the DFE among all
mutations, and beneficial mutations in particular.
Second, the theory, in its current form, does not make any
predictions about the joint fitness effects of beneficial
mutations across several novel environments. In particular,
one would like to know to what extent mutations that
improve fitness in one set of conditions also improve it in
others. Are the pleiotropic effects of new mutations in
different conditions also jointly exponentially distributed?
Do beneficial mutations tend to be ecologically specialized—
that is, beneficial in a narrow range of environments—or do
they tend to maintain high fitness across a broad range of
conditions? Knowing the direction and magnitude of the joint
fitness effects among beneficial mutations is crucial for understanding the evolution of niche specialization. It is also
important in an applied context: when pathogens become
resistant to antibiotics or antiviral drugs (that is, gain a beneficial mutation), how large a cost of resistance should we
expect to see? The answer matters because the cost of resistance is an important factor governing the prevalence of
resistance in the absence of antibiotic (Lipsitch et al. 2000)
and so can be used to guide treatment strategies.
Third, an exponential is predicted under EVT only if the
underlying DFE of all mutations is in the so-called Gumbel
domain of attraction. Beisel et al. (2007) have pointed out
that there are actually two other domains of attraction predicted by EVT: the Fréchet domain containing distributions
with tails that are heavier than the exponential and the
Weibull domain containing distributions that are bounded
on the right. Neither of these distributions converge to an
exponential, although they can look exponential-like (L
shaped). Efforts to identify which distribution best describes
empirical data have been undertaken with bacteria (Kassen
and Bataillon 2006; Maclean and Buckling 2009; McDonald
et al. 2010) and viruses (Rokyta et al. 2008), but the results
are conflicting because studies of beneficial mutations com-
940
T. Bataillon, T. Zhang, and R. Kassen
prise very few mutants and attention has been focused on
relatively few environments: only four in Kassen and Bataillon
(2006) and one in the remainder.
Fourth, recent theoretical work has derived the full DFE
among mutations in Fisher’s geometric model (FGM) under
the assumption that mutations pleiotropically affect a set of
quantitative traits that are under stabilizing selection with
fitness declining as a Gaussian function of the distance of
a genotype to an optimum. Under this model, the DFE of
new mutations is well approximated by a displaced gamma
distribution, where the magnitude of the displacement is a
measure of how mal-adapted the initial genotype is (Martin
and Lenormand 2006). The DFE among beneficial mutations
in this model can be markedly different from those in an
exponential model, although T converges to an exponential
one when fitness is underlain by a large number of independent traits. Martin and Lenormand (2008) have derived a
b-approximation for the (scaled) distribution of beneficial
mutations under FGM that falls within the Weibull domain
of EVT.
Here we address each of these issues empirically by using
a subset of a large library of single-step resistance mutants in
P. fluorescens previously used by Kassen and Bataillon
(2006). Specifically, we are interested in the following four
questions: (1) What are the effects of beneficial mutations
on the degree of niche specialization? This question is
one component of the larger issue concerning the extent
to which single mutations contribute to G·E interaction
(Remold and Lenski 2001). (2) How general is the prediction of an exponential DFE? We test this prediction directly.
(3) Does a simple fitness landscape model such as FGM
provide an adequate description of the DFE among all mutations, including beneficial ones? (4) How robust are the
predictions of FGM to the inclusion of at least some genotypes that carry multiple mutations? To answer these questions, we make use of two subsets of mutants reported in
Kassen and Bataillon (2006)—those that were previously
identified as being beneficial (hereafter referred to as the
“top 18” mutants) in the same environment in which resistance was selected and a collection of 63 mutants collected
at random without regard to their fitness under the original
test conditions (hereafter referred to as the “random 63”).
For both subsets, we assay the fitness of these mutants,
together with the ancestral strain, across a wide range of
novel environments, each differing in the carbon substrate
available for growth.
Materials and Methods
Mutant strains
The protocol for mutant collection is given in Kassen and
Bataillon (2006). Briefly, a collection of 673 independently
derived strains containing mutations conferring resistance
to the quinolone antibiotic nalidixic acid was obtained by
screening .2000 populations of the wild-type strain SBW25
of P. fluorescens in a conventional fluctuation-style assay.
This method permits the collection of novel genotypes derived from independent mutational events occurring naturally during population expansion without regard to their
fitness effects in the assay environments. The primary targets of chromosomal quinolone resistance in Gram-negative
bacteria are the DNA gyrases, GyrA and GyrB, where point
mutations in a highly conserved region (the quinolone resistance determining region, or QRDR) within gyrA and gyrB
are especially common, and topoisomerase IV, porins, or
efflux systems (Bagel et al. 1999; Jalal et al. 2000; Kohler
and Pechere 2001). Although we have not undertaken an
exhaustive analysis to identify all possible sites conferring
resistance in our collection, we have found five distinct nonsynonymous mutations in 15 of the 18 strains sequenced
from a 500-bp region of the QRDR of gyrA (Table 1). Four
mutations are substitutions in either amino acids 83 (Thr) or
87 (Asp), which are among the most common sites associated with resistance to quinolones in clinical isolates of Pseudomonas aeruginosa (Wong and Kassen 2011), and one is at
position 81 (Gly). Additional sequencing and phenotypic
assays (see below and Table 1) reveal at least 15 unique
genotypes in our top 18 collection.
We assessed the prevalence of second-site mutations in
our top 18 mutant collection using two approaches. First, we
sequenced the QRDRs of gyrB, parC, and parE and the putative efflux pump regulatory sites mexAB, mexCD, mexEF,
and an additional unidentified mex-family regulator. Putative efflux pump transcriptional regulators were identified as
transcription factors situated immediately upstream of mextype multidrug efflux pump operons. As efflux pump systems
in P. fluorescens are poorly characterized, we pinpointed
orthologs of the P. aeruginosa MexAB-OprM, MexCD-OprJ,
and MexEF-OprN efflux pumps in the P. fluorescens SBW25
genome using BLAST analysis. Primers used for sequencing
are available from the authors upon request. Second, we
assayed for efflux pump-mediated resistance by examining
the difference in minimum inhibitory concentration (MIC)
to nalidixic acid in the presence and absence of Phe-Argb-napthylamide (PAbN). PAbN, also referred to in the literature as MC-207-110, was first identified as an inhibitor of
three resistance-nodule-division multidrug efflux pumps
(MexAB-OprM, MexCD-OprJ, MexEF-OprN) in P. aeruginosa
(Lomovskaya et al. 2001). PAbN enhances the effect of
a number of antibiotics including fluoroquinolones, chloramphenicol, oxazolidinones, and rifampicin. It is believed
that PAbN acts as a competitive inhibitor of antibiotics by
binding to antibiotic-binding sites within membrane transporter proteins, thus impairing antibiotic efflux (Lomovskaya and Bostian 2006). We estimated the minimum
number of mutations for a given strain by first grouping
mutants according to their gyrA genotype and then by examining each of these for the presence of second-site mutations at all non-gyrA targets. For those strains where no
second-site mutations were found, we then compared the
PAbN phenotype to that of the wild type using two-tailed
t-tests. A significant difference in MIC in the presence and
absence of PAbN relative to the wild type was taken as
evidence of an additional mutation affecting resistance.
Fitness assays
All strains, including the nalidixic acid-sensitive ancestor,
SBW25, were first streaked to single colonies from frozen
cultures and then grown overnight at 28 in liquid media
containing 5 ml of Luria–Bertrani [LB; 10 gL-1 (grams
per liter) bacto-tryptone, 5 gL-1 yeast extract, 10 gL-1 NaCl]
medium. Resistant strains were grown in the presence of
antibiotic (100 mlml21 nalidixic acid). Aliquots of 50 ml
from overnight cultures were then starved for 2 hr in
50 ml of M9 minimum salts (1 gL-1 NH4Cl, 3 gL-1 KH2PO4,
0.5 gL-1 NaCl, 6.8 gL-1 Na2HPO4, supplemented with
15 mgL-1 CaCl2 and 0.5 gL-1 MgSO4) while being shaken
at 150 · g at 28. A total of 150 ml from the starved cultures
was then inoculated into each well of commercially available microwell plates containing 95 different carbon substrates (Biolog), and the optical density (OD) was read at
630 nm with an automated microwell plate reader. Cultures
were allowed to grow, unshaken, at 28 for 48 hr and the
OD was read again. Fitness was estimated as the difference
between the final and initial OD readings (DOD). All assays
were conducted in triplicate, giving a total of (19 strains ·
3 replicates) + (64 · 3 replicates) = 249 Biolog plates for
both experiments.
PCR amplification and sequence determination
Primers were designed to amplify the fragments of gyrA positions 1–791, gyrB positions 1268–2000, parC positions 1–
797, and parE positions 1120–1905 containing the P. fluorescens QRDR region, and primers for the putative efflux pump
regulators were designed to amplify the entire gene. The PCR
amplification protocol composed of denaturation for 5 min at
95 and then 35 cycles of denaturation for 30 sec at 95,
annealing for 30 sec at a temperature between 55 and 65
that was optimized for each gene, elongation for 1 min at 72,
and a final elongation step for 10 min at 72. The reactions
were carried out in a 50-ml volume with 2.5 units of Taq DNA
polymerase (Invitrogen). The PCR-amplified DNA was sent to
the Genome Québec Innovation Centre at McGill University
for sequencing on the forward strand, and mutations were
identified using BLAST analysis against the SWB25 genome
(GenBank accession no. AM181176).
Efflux pump inhibition assay
MIC analysis was performed in cation-adjusted Mueller–
Hinton broth in 96-well microtiter plates following a
microbroth dilution method adapted from the National
Committee for Clinical Laboratory Standards protocol
(Schwalbe et al. 2007). An inoculum density of 5 · 105
cfu/ml was employed in all experiments, and nalidixic acid
MIC values for the wild-type and mutant strains in the presence or absence of 5 mg/ml of the efflux pump inhibitor
PAbN were determined in two replicates following a 24-hr
incubation period at 28.
G·E and DFE of Beneficial Mutants
941
Table 1 DNA sequence variation among the top 18 mutants
Strain
Fitness rank
in LB
gyrAa,b
SBW25
3-1-B1
1-5-D8
19
4
7
—
—
—
2-10G10
1-7-F5
1-4-B9
15
—
1-8-G4
1-6-F8
2-9-H4
1-1-H10
11
12
3
6
2-4-A12
2-8-F7
1-10-H10
1-1-G1
2-8-F8
3-1-A6
1-6-A9
1-8-A1
2-7-C3
8
10
13
17
5
9
14
16
18
2
1
Second-site
mutationsc
—
NA
mexCD regulator:
Leu134Phe
(C514G)
NA
Asp87Ala (GAC260GCC) NA
Asp87Gly (GAC260GGC) mexAB regulator:
GC ins stop codon
at AA 44
Asp87Gly (GAC260GGC) NA
Asp87Gly (GAC260GGC) NA
Asp87Tyr (GAC259TAC)
—
Asp87Tyr (GAC259TAC) mexEF regulator:
Ser88Asn (G863A)
Asp87Tyr (GAC259TAC)
—
Asp87Tyr (GAC259TAC) NA
Asp87Tyr (GAC259TAC) NA
Asp87Tyr (GAC259TAC) NA
Gly81Cys (GGC241TGC)
—
Thr83Ile (ACT248ATT)
NA
Thr83Ile (ACT248ATT)
NA
Thr83Ile (ACT248ATT)
NA
Thr83Ile (ACT248ATT)
mexAB regulator:
Arg90His (G269A)
Fold increase in
Difference in
minimum inhibitory log(MIC) following Minimum
concentration (MIC) addition of efflux number of
to nalidixic acid
inhibitor d,e
mutations
Genotype
classf
1
NA
47.4
0.798 6 0.177
NA
1.457 6 0.129**
0
1
1
Wild type
A
B
NA
NA
1
A
47.4
47.4
1.545 6 0.116**
0.088 6 0.173**
1
2
C
D
25.2
25.2
25.2
101.0
1.007
0.968
0.304
0.389
6
6
6
6
0.128
0.173
0.128*
0.112*
1
1
1
2
E
E
F
G
101.0
21.0
101.0
25.2
56.8
31.6
19.9
101.0
56.8
0
0.576
0
0.176
1.537
0
0.401
0.908
0
6
6
6
6
6
6
6
6
6
0**
0.128
0**
0.245*
0.208*
0.164**
0.208*
0.210
0**
2
1
2
1
1
1
1
1
2
H
I
H
J
K
L
M
N
O
—, identical to wild type (SBW25).
NA, not sequenced or data not available.
Sequences assayed were the QRDR of gyrB, parC, and parE, as well as the DNA-binding sites of the putative efflux pump regulators mexAB, mexCD, mexEF, and a generic
mex-family regulator; see Materials and Methods for details.
d
Values shown are mean difference in log(MIC) without and with the efflux inhibitor, PAbN 6 95% confidence intervals; see Materials and Methods for details.
e
Significant from SBW25 at *P , 0.05. Significant from SBW25 following Bonferroni correction for 16 tests such that **P , 0.003.
f
Genotypes sharing the same letter are putatively identical on the basis of direct sequencing and the efflux inhibitor assay. Wild type is the genome of the ancestral, nalidixic
acid-sensitive SBW25 strain from which all strains are derived.
a
b
c
Niche specialization among the top 18 mutants
We assayed the degree of niche specialization in two ways.
First, we counted the number of environments on which
each beneficial mutant grew relative to the ancestral strain.
Second, for each strain we calculated its fitness effect, which
was the difference in fitness between a mutant strain and
the ancestor, in each environment and then took the average
fitness effect for each strain across all environments. We
omitted from this analysis any environments where the
mutant strain grew but the ancestor did not.
Genotype-by-environment interaction
We performed a two-way ANOVA with strains and environment as random main effects. From this we calculated the
variance components associated with each main effect and
their interaction by equating expected with observed mean
squares using the lmer function in the lme4 package in R
(R Development Core Team 2009). These calculations were
done by including only environments in which a strain
showed evidence of growth assessed as a mean OD that
was greater than twice the standard deviation of OD meas-
942
T. Bataillon, T. Zhang, and R. Kassen
urements taken from the blank well of a BIOLOG plate. The
sensitive ancestor, SBW25, was omitted from this analysis.
We further decomposed the G·E interaction variance, VGE,
using Robertson’s (1959) equation for the G·E between
any pair of environments: VGE = 1/2 (SG1 – SG2)2 + SG1SG2
(1 2 rG1G2), where SGi is the genetic standard deviation in
environment i, and rG1G2 is the cross-environment genetic
correlation. In this model, (SG1 – SG2)2 expresses the
squared difference in the amount of genetic variation between the two environments. We regressed VGE against
the squared difference in average performance between
a pair of environments, which represents macroenvironmental variance expressed by the same collection of genotypes
tested in a pair of environments. We assessed the significance of the slope of the regression in each case using a randomization procedure (1000 randomizations were used)
written in R (R Development Core Team 2009).
Analysis of the DFE among beneficial mutants
Irrespective of statistical significance within each environment, we deem as “beneficial” all mutant genotypes that
had a higher mean fitness than the ancestral genotype. We
first analyzed our data sets under the assumption that all
mutants contain a single mutation affecting fitness. We then
examined the robustness of our inferences about the DFE in
the presence of contamination by second-site mutations (see
Monte Carlo simulation of DFE expected in empirical data
sets). Instead of relying on the likelihood ratio test (LRT)
developed by Kassen and Bataillon (2006), we used a likelihood framework developed by Beisel et al. (2007) that
allows testing of the exponential against other domains of
attraction predicted by EVT. In particular, we obtained the
empirical DFE in each BIOLOG environment by scaling mutation effects relative to the smallest beneficial mutations
instead of the ancestral type. This shifting procedure is
expected to make our analysis much more robust to missed
beneficial mutations and only “costs” 1 d.f. by decreasing the
sample size by 1 in each environment. Within each environment, we obtain the likelihood of our data (our observation
consisting of the shifted beneficial mutation effects) under
a generalized Pareto model with two parameters (shape and
scale). A formal test for the hypothesis that the DFE of beneficial mutations is exponential is conducted using a LRT
comparing the likelihood of the full model with that of a reduced model (scale parameter k set to zero in the exponential case). A P-value for the LRT is obtained by parametric
bootstrapping (10,000 boostrap samples from an exponential with the fitted scale were used). The analysis of the data
was done in R [R Development Core Team (2009)].
Given that each test is performed on a small sample size,
we conducted a pooled test across environments where at
least six beneficial mutations were detected. Briefly, within
each environment i, a P-value pi is collected for the LRT described above. Under the null hypothesis that the DFE of beneficial mutation is exponential in all k environments, the pi’s
are uniformly distributed between 0 and 1, and the statistic
L = 22 Si ln(pi), with i = 1..k, is distributed as a x2 with 2k d.f.
Finally, we consider the predictions about the DFE among
beneficial mutations using FGM under the assumption that
the wild type is close to an optimum (Martin and Lenormand 2008). We first rescaled the data using the largest
beneficial mutant as a proxy for the distance to the optimum
and then fit a constrained b-distribution Be[a = 1, b] to this
rescaled data. We compare the fit of the constrained b to
a fit with two free parameters (the shape parameter a is also
free to vary) using a LRT. Note that this procedure should
not be interpreted as a test of the fit of an explicit landscape
model against any other model such as those that assume
only EVT conditions. This is because both models make the
same underlying assumption that the wild-type genotype is
initially well adapted and, moreover, that the two models
converge when the number of independent characters determining fitness is large.
Monte Carlo simulation of DFE expected in empirical
data sets
We examined how the presence of second-site mutations
affected our ability to infer the DFE among beneficial mu-
tations by first simulating the DFE expected under ideal
conditions (all mutants are exactly one mutational step
away from the wild type) and under “less than ideal,” but
more realistic, conditions where the collection of mutants
comprises a mixture of true single-step mutations and those
carrying extra mutations influencing fitness. To simulate the
DFE, we used a fitness model based on FGM. The rationale
for this choice is twofold. First, FGM generates explicit predictions about epistasis and the DFE among mutants carrying an arbitrarily large number of mutations (Martin et al.
2007), something that the mutational landscape model
cannot easily do. Second, because we have fit our data to
a landscape model generated using predictions obtained
under ideal conditions, it provides a natural means of assessing the degree to which contamination by double mutants
changes the DFE.
Simulations followed the parameterization of FGM described in Martin et al. (2007), and we examined different
scenarios by varying the effective number of dimensions of
the landscape (m), the mean fitness effect of a single mutation, E(s), and the initial distance to the optimum (so). To
obtain the DFE of all mutants, we simulated the fitness of
100,000 independent mutants carrying 1 + c mutations
affecting fitness, where c is a stochastic number of “contaminating” mutations. Following the description of our procedure for isolating mutants, we assumed that c was Poisson
distributed with a mean l. Thus, l = 0 generates the case of
pure single-step mutants while l = 0.5 represents the less
than ideal condition of allowing for double mutants at a rate
that roughly matches, and may even be higher than, the
proportion of mutants carrying more than a single fitness
affecting a mutation uncovered in our samples (see below).
We then studied how the shape of the DFE, k, associated
with beneficial mutations was affected by the presence of
multiple mutations. We focused on k as it is of central interest in characterizing beneficial mutations. We examined
how k changes with different combinations of the parameters determining the DFE [m, so, E(s), l] by sampling 10–20
mutants from each of 1000 simulated data sets for each
distribution and re-estimating the shape parameter k.
Results and Discussion
DNA sequence variation among top 18 mutants
We used both sequencing and a phenotypic assay in an
effort to identify the genetic targets of quinolone resistance
in our top 18 mutants. Our results are reported in Table 1.
As is often observed in clinical strains of Gram-negative bacteria resistant to quinolones, all but three strains contained
mutations in the QRDR of gyrA. Within this site we found
five distinct mutations, four of which occur at two amino
acid sites (83 and 87) known to be associated with binding
of GyrA to DNA (Wong and Kassen 2011). No further mutations were found at the sites often associated with the primary incidences of quinolone resistance—gyrB, parC, or
parE—among the subset of the top 18 chosen for further
G·E and DFE of Beneficial Mutants
943
sequencing. We did, however, uncover four additional
unique mutations in putative regulators of efflux pumps,
three of which occurred alongside a gyrA mutation. These
results, combined with our phenotypic assay, suggest that
we have at least 15 unique strains and five double mutants
in our collection. Note that this assay is conservative because
we have examined only those sites that are known or
thought to be involved in conferring resistance to quinolones. Recent efforts to identify alternative genetic targets
of resistance to the fluoroquinolone ciprofloxacin in P. aeruginosa, a close relative of P. fluorescens, suggest that there
may be .40 additional genes capable of conferring a more
than twofold reduction in susceptibility as measured by MIC
(Breidenstein et al. 2008). Given this wide range of putative
resistance targets, we suspect that the majority, if not all, of
our strains are genetically unique as required by theory.
That being said, we have also clearly violated the assumption that all mutants in our collection are a singlenucleotide step away from the wild type, with at least 28% of
our strains carrying second-site mutations. This is likely to be
something of an underestimate because, by design, we have
searched for double mutants only at those sites known to be
clinically important for conferring resistance to quinolones
and fluoroquinolones in related species. If genomic mutation
rates are indeed higher than previously thought, we may have
missed second-site mutations occurring elsewhere in the
genome. The observation of double mutants is not unusual,
at least among clinical isolates of P. aeruginosa. Wong and
Kassen (2011) showed that clinical isolates of fluoroquinolone-resistant P. aeruginosa often contain multiple mutations
to both gyrases and efflux pumps and that the identity of the
efflux pump mutation depends on whether the infection is
acute or chronic. Although it is unlikely that double mutants
arise simultaneously in clinical strains, the fact that they do
happen at all suggests that having more than one resistanceassociated mutation confers a fitness advantage. Our results
(Table 1) indicate that double mutants in our collection have
MICs to nalidixic acid that are nearly 10· higher than single
mutants (Welch’s one-tailed two sample, t10.6 = 3.66, P =
0.002). However, double mutants did not tend to have higher
fitness ranks in LB than single mutants (Welch’s one-tailed two
sample, t6 = 0.128, P = 0.549), nor was there any detectable
relationship between the MIC conferred and the fitness rank
in LB among strains in general (slope 6 standard error =
20.006 6 0.030, F1,14 = 0.046, P = 0.832). Taken together,
these results suggest that, although the second-site mutations
that we identified tend to substantially decrease susceptibility
to nalidixic acid, they contribute little to the variation in fitness
in the absence of a drug. Below we consider in more detail
how the occurrence of such double mutants might impact
inferences about the DFE among mutations.
Most beneficial mutants do not pay a substantial cost of
adaptation in new environments
We used several indicators to quantify the amount of
ecological specialization associated with the set of 18
944
T. Bataillon, T. Zhang, and R. Kassen
mutants deemed beneficial in the original LB environment.
First, we characterized the niche breadth of a genotype as
the number of carbon sources that it effectively utilizes. The
ancestral type grew on 55 of the 95 carbon sources available. With the exception of one mutant genotype (which lost
the ability to grow in .10 environments relative to wild
type), all other beneficial mutants had a niche breadth similar to wild type (Figure 1A). Second, we calculated a mean
fitness effect, relative to the wild type, of each mutant across
all environments (where growth was available). We found
no relationship between the mean fitness effect of a mutant
across environment and the fitness rank of the mutant in
permissive LB media, the media in which beneficial effects
were assessed in Kassen and Bataillon (2006) (Figure 1B).
Taken together, these results suggest that a mutant beneficial in one environment is not substantially deleterious in
other environments. Thus, specialization underlain by a cost
of adaptation (i.e., the loss of fitness in the original environment relative to the ancestor) is unlikely to evolve in a single
mutational step; rather, it will require the substitution of
multiple beneficial mutations.
Patterns of G·E interaction among single-step mutants
do not differ significantly between beneficial mutants
and a random sample of mutants
We contrasted patterns of G·E interactions in the set of 18
mutants previously deemed beneficial in LB medium and
a set of 63 mutants selected at random from the library of
resistant strains. Notably, the random 63 mutants displayed
a wide range of fitness values that included both deleterious
and beneficial effects in LB. If there is something unusual or
distinct about the fitness effects of these beneficial mutations
in our top 18 collection in novel environments, then we
should see this reflected in the pattern of G·E variance between the two sets of strains. Overall, the fraction of genetic
variance attributable to G·E (VGE) effects was similar between the two sets: VGE accounted for 21 and 32%, respectively, of the total genetic variance in the top 18 and the
random 63 data sets. The top 18 set therefore does not exhibit any extraordinary amount of VGE relative to the subset
random 63. This was confirmed by a second analysis where
we considered pairs of environments and examined how VGE
changed with the macroenvironmental variance between
each pair of environments. In both cases, VGE increases as
the macroenvironmental variance between a pair of environments increases, as has been observed previously (Kassen and
Bell 2000), but there is little difference in the slope of this
relationship for each subset (Figure 2). Together, this suggests that beneficial mutants are neither more canalized nor
more reactive than a random sample of comparable mutants
when exposed to the range of novel environments used here.
It is notable that the magnitude of VGE is on the same
order as that found using a small set of random insertion
mutants in Escherichia coli (Remold and Lenski 2001) or in
agronomic studies using a set of genotypes that are
Figure 1 Patterns of ecological specialization of the 18 beneficial mutations. (A) Distribution of number of environments showing growth in the
top 18 mutants. Note that the niche breadth of the ancestral type is at
the mode of the distribution (i.e., could grow in 55 environments). (B)
Mean fitness effects (averaged across all carbon sources) of the top 18
mutants. Rank is based on the performance in the initial environment
(LB). Symbols designate known (to date) mutations in the 500-bp region
of the gyrA QRDR: h, Asp87Gly; s, Asp87Ala; ,, WT; ), Asp87Tyr; n,
Thr83Ile.
potentially a lot more divergent genetically (Bell 1997). We
have at present no compelling explanation for this finding,
except to say that this reinforces the conclusion that there is
little that is distinctive about the top 18 mutants that were
beneficial in LB.
DFE of beneficial mutants is not universally exponential
across environments
In 32 of 95 environments, at least six mutants among the
top 18 were found to be better than SBW25, irrespective of
formal tests of significance. We asked whether, in these
environments, the exponential provided an adequate fit to
the empirical distribution of fitness effects among beneficial
mutants. We tested whether the shape parameter (k) of a
Figure 2 Distribution of fitness effects among pure vs. contaminated
mutant genotypes. All distributions are based on the simulation of
100,000 independent mutant genotypes under the assumption of FGM
parameterized as described in Materials and Methods. Note that for
graphical convenience we do not display these empirical distributions as
histograms but report here smoothed distributions. Orange: DFE of pure
single-step mutant genotypes (ideal conditions) Gray: DFE of mutant genotypes carrying one mutation affecting fitness plus a Poisson-distributed
number of extra mutations (rate of contamination, l ¼ 0.5). This generates
a mixture of pure single-step mutants contaminated with genotypes carrying extra mutations affecting fitness. (A) m ¼ 5; E(s) ¼ 0.01; so ¼ 0.05. (B)
m ¼ 5; E(s) ¼ 0.01; so ¼ 0.01. (C) m ¼ 2; E(s) ¼ 0.01; so ¼ 0.05; Poisson
rate of contamination, l ¼ 0.5. (D) m ¼ 2; E(s) ¼ 0.01; so ¼ 0.01; Poisson
rate of contamination, l ¼ 0.5.
generalized Pareto distribution (GPD) estimated from the
data differed significantly from that expected under an exponential distribution (k = 0). We estimated the shape parameter using both the maximum likelihood (ML) estimator
of Beisel et al. (2007) on (rescaled) data and an alternative
estimator proposed by Rokyta et al. (2008). In all environments, estimates for the shape parameter of the GPD distribution are negative and occasionally smaller than 21
(Figure 3B), suggesting that a right-truncated distribution
(whether J or L shaped) provides a better a fit of the data
than an exponential distribution. Due to low sample size in
each environment (from n = 6 to n = 13), the null hypothesis
of an exponential distribution could rarely be rejected (of 32
tests, only 5 tests had a P-value ,5% before correction for
multiple testing). However, combining tests across 32 environments strongly rejects the global null hypothesis of an
exponential distribution across all environments (P ,
0.001; see also Figure 3A for distribution of P-values). These
results are consistent with re-analyses of two viral data sets
(Rokyta et al. 2008). Taken together, these results suggest
that the DFE among beneficial mutants is not exponential
G·E and DFE of Beneficial Mutants
945
Figure 3 Meta-analysis of the DFE
across environments. (A) Distribution of
P-values associated with the test of the
departure from an exponential DFE in
each environment. The horizontal line
denotes the expected counts of P-values
in each bin on the basis of the global
null hypothesis that DFE is exponential
in every environment. (B) Distribution
of the shape parameter, k, of the DFE
of beneficial mutations in each environment. k was estimated in each environment using an estimator proposed by
Rokyta et al. (2008) that is more accurate than maximum-likelihood estimates
when the shape parameter is negative.
(C) Distribution of P-values associated
with LRT for the departure from the null
hypothesis of a constrained b-distribution for DFE in each environment. The
horizontal line denotes the expected
counts of P-values in each bin based
on the global null hypothesis that DFE
is a constrained b, Be[1,b], in every environment. (D) Distribution of the effective number of independent phenotypic
traits, m, describing Fisher’s geometric
landscape in each environment. Estimates of m are based on the theoretical
relationship between m and the shape
parameter (k) of the DFE of beneficial
mutations (k).
but is, rather, located in the so-called Weibull domain of the
GPD (shape parameter k , 0) where the distributions are
right truncated. It is further notable that two recent studies
on the DFE of new mutations in P. fluorescens (McDonald
et al. 2010) and P. aeruginosa (Maclean and Buckling
2009) also strongly reject the exponential, although in these
cases the wild-type strain was initially very maladapted, and
so EVT arguments are, a priori, expected to perform poorly.
Can a simple fitness landscape model predict the DFE
of beneficial mutations?
Martin and Lenormand (2008) derived a b-approximation
for the DFE of beneficial mutations using an explicit fitness
landscape model featuring a single smooth fitness peak. Fitting their model requires that we know the distance of the
initial genotype to the fitness optimum. Using the fitness
effect of the largest mutant as a proxy for the distance to
the optimum [a similar approximation is effectively used by
Rokyta et al. (2008) to derive their alternative estimator for
the shape parameter of the GPD], we first rescaled our data
by this value and then fit the rescaled data to a b-distribution
constrained to be Be[1, b]. Comparing the fit of this model to
a nonconstrained b allows us to ask directly whether the
fitness landscape model provides an adequate fit to the data
in each environment.
Keeping in mind that our procedure for rescaling the data
to obtain an estimate for distance to the optimum is rather
crude, the constrained b predicted under a fitness landscape
946
T. Bataillon, T. Zhang, and R. Kassen
model does seem to provide an acceptable fit in many environments: the constrained b-model is rejected in favor of the
nonconstrained b-model in only 5 of the 32 environments
(using a 5% level without correction for multiple tests).
Note again, however, that, although the empirical distribution of P-values associated with the test above is fairly flat
(Figure 3C), a combined test pooling P-values across all
32 environments again rejects the composite null hypothesis that data in all environments is compatible with the
constrained b (P , 0.01). Further work is needed to infer
more rigorously the parameters of a fitness landscape from
empirical data. One can also, in principle, use the shape parameter of the empirical DFE to make an approximate inference about m, the number of effectively independent traits
underlying the fitness landscape in each environment. Here
our analysis suggests that m is not very large, being as small
to 2–4 in the majority of environments (Figure 3D). This
squares nicely with theory by Martin and Lenormand
(2008) showing that, under the assumption of their fitness
landscape model, the DFE among beneficial mutations will be
well approximated by an exponential only if a relatively large
number of independent traits underlie fitness.
Inferences about the DFE among beneficial mutations
are robust to contamination with multiple mutations
Our results may be criticized because our top 18 data set
violates the assumption that all mutants are a single
mutational step away from the wild type. This may not be so
surprising in retrospect if, as seems to be the case, genomic
mutation rates are two to three times higher than previously
thought. However, it does call for caution when interpreting
the results of experiments such as ours that have used
fluctuation-style assays to “trap” mutations of interest in target genes, as these cannot always be assumed to be single
mutants (see especially Maclean and Buckling 2009).
How robust are our inferences about the DFE and
contamination by double mutants? Intuition suggests that
the realized DFE of a collection of single and double mutants
can be interpreted as the DFE among true single-step
mutations with the addition of draws from the DFE of
mutants carrying two mutations or more. Stochastic simulations under FGM (the fitness landscape model used above
to fit our data) confirm this intuition (Figure 4; see also
Martin et al. 2007). For rates of contamination compatible
with our data, the DFEs containing true single-step mutations and those contaminated by multiple mutations are
actually quite similar, with estimates of k (which characterizes the DFE of beneficial mutations) from small data sets
(10–20 mutants) being very similar between ideal and contaminated data sets (Table S1). Thus empirical tests of theory appear to be fairly robust even when violating the
assumption that all mutants are a single mutational step
from the wild type, which will likely be the case when trapping large numbers of mutants with the type of assays described above. Finally, there is little reason to think that the
presence of double mutants in our data set severely biases
our most important conclusion—that the DFE among beneficial mutants is not exponential but located in the Weibull
domain of the GPD (shape parameter k , 0) as the sign of k
is always negative even if the values themselves are slightly
different.
Conclusion
The development of a predictive theory of adaptive evolution has benefited from the analysis of both sequence- and
phenotype-based models. Empirical evaluation of these models has been hampered, however, because beneficial mutations
are so rare that sample sizes tend to be small and the inferential strength of these tests remains modest at best.
To begin to redress this lack of data, we have assayed the
fitness of a sample of mutants that had previously been
found to be beneficial in a single environment across a large
array of new environments. This procedure allows us both to
describe the pattern of niche breadth—a key ecological characteristic for understanding the evolution of specialization
and the maintenance of diversity—and to provide a more
comprehensive test of the theoretical predictions regarding
the DFE among beneficial mutations.
In terms of niche characteristics, our main finding is that
the mutants that we had previously identified as beneficial
in one environment are not severely compromised in fitness
in a wide range of alternative environments. Indeed, there is
Figure 4 Comparison of the effect of environmental contrast on the
amount of variance due to G·E, VGE, in both data sets. The macroenvironmental contrast is calculated as the squared difference in mean performance in each environment (averaged across the set of strains).
little evidence for strong costs of adaptation relative to the
antibiotic-sensitive wild type in different environments;
most mutants deemed beneficial in LB (the environment in
which they were originally selected) remain beneficial, or at
least neutral, across a wide range of environments. A similar
result has been observed for mutants conferring a fitness
advantage in a minimal glucose environment in E. coli
(Ostrowski et al. 2005), suggesting that our results are not
unique for being resistance mutations. Moreover, the quantity
of VGE in this mutant collection does not appear to be unusual
in any way, either when compared to a larger random sample
of resistant mutants from the same library that includes many
deleterious strains or when compared to similar analyses performed on widely different organisms (Bell 1997).
These results have at least two important implications.
First, the evolution of specialization underlain by costs of
adaptation is unlikely to occur through the substitution of
a single mutation. Costs of adaptation, when they are found,
are likely to be built up through the substitution of multiple
mutations contributing to adaptation. Perhaps this result is
not surprising, but it does provide an explanation for why
strong fitness trade-offs and large costs of adaptation do not
readily evolve in most laboratory selection experiments
lasting between a few hundred and a thousand generations
(reviewed in Kassen 2002). The timescale of these experiments is simply too short for large costs of adaptation to
evolve. Second, to the extent that antibiotic resistance is
attributable to single or double mutants that arise rapidly
under antibiotic selection, our efforts to eliminate or control
resistance must do more than simply halt the use of the
offending antibiotic. Costs of resistance, which are a special
case of costs of adaptation, are not likely to be of sufficient
magnitude to eliminate resistant strains through competition with a sensitive wild type alone. Alternative strategies
G·E and DFE of Beneficial Mutants
947
Figure 5 Diversity of shapes for the
scaled DFE of beneficial mutations. Each
curve represents the constrained b-distribution best fitting the scaled empirical
DFE of beneficial mutants in each environment (n ¼ 32). All DFE predicted under the FGM model have a right tail that
is truncated but, depending on the underlying number of dimensions, m, the
distributions assume a variety of shapes.
Distributions with m . 2 are essentially L
shaped. When m ¼ 2, distributions are
flat (uniform). DFE can even be J shaped
(when m , 2).
that use antibiotic cycling or multidrug cocktails are likely to
prove much more effective.
What of the DFE among beneficial mutations? By assaying
the fitness of a collection of mutants across many different
environments, we have obtained a large collection of DFEs
among beneficial mutants. This approach allows us to
sidestep two problems at once. On the one hand, it alleviates
the pervasive issue of small sample sizes. Instead, we now
have many DFEs, even if each one may still be based on small
sample sizes within a given environment. At the same time,
this approach means that we do not have to be overly
concerned with what the “natural” environment is for our
mutants. Rather, we can ask the more general question,
how variable is the DFE among beneficial mutants across
environments, given that the wild type is fairly well adapted?
The empirical picture emerging from our study is quite
clear: the DFE among beneficial mutants is one that is
characterized by many mutations of small effect and few of
large effect. This, again, is not surprising. But, importantly
for theory, this distribution is located within the Weibull
domain of attraction, not the Gumbel domain as has
previously been thought. It is important to note that a wide
range of k-values within the Weibull can give rise to decreasing distributions that can, at first glance at least, resemble an exponential (Figure 5). The broad similarity
among these alternative distributions notwithstanding, our
meta-analysis confirms the results of previous work in bacteria (Maclean and Buckling 2009; McDonald et al. 2010),
948
T. Bataillon, T. Zhang, and R. Kassen
phage (Rokyta et al. 2008; Miller et al. 2011), and filamentous fungus (Schoustra et al. 2009) that the DFE among
beneficial mutations is not exponential but is instead characterized by having a truncated right tail. Moreover, these
conclusions are not severely compromised by the fact that
our mutant collection contained some strains that carried
two mutations. Our simulations of the DFE under a fitness
landscape model suggest that estimation of the shape parameter for the DFE among beneficial mutants is fairly robust to violating the assumption that all mutations are
a single step away from the wild type. An alternative approach might be to follow that of Martin and Lenormand
(2008) and use a b-distribution to characterize the scaled
DFE among beneficial mutations. Our results suggest that
this approach may work quite well. Future work should
focus on theory to quantify the joint DFE of new mutations
in multiple environments and the development of a theoretical framework to understand the DFE in populations that
are both initially well or poorly adapted.
Acknowledgments
We thank G. Martin for sharing unpublished R code for
efficient simulation of Fisher’s geometric landscape, M.
Al-Azzabi for technical help, two anonymous reviewers, and
Jim Bull for comments. T.B. was supported for part of this
work by a Steno fellowship awarded by the Danish Council
for Independent Research in the Natural Sciences. R.K. was
supported by grants from the Natural Sciences and Engineering Research Council of Canada. T.B. and R.K. also acknowledge the French Embassy in Ottawa for additional funding.
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G·E and DFE of Beneficial Mutants
949
GENETICS
Supporting Information
http://www.genetics.org/cgi/content/full/genetics.111.130468/DC1
Cost of Adaptation and Fitness Effects of Beneficial
Mutations in Pseudomonas fluorescens
Thomas Bataillon, Tianyi Zhang, and Rees Kassen
Copyright © 2011 by the Genetics Society of America
DOI: 10.1534/genetics.111.130468
Table
S1
Estimation
of
the
shape
parameter
estimates
(κ)
of
DFE
of
beneficial
mutations
in
ideal
and
contaminated
datasets.
b
m
E(s)
S0
λ contamination
nsample
Mean
κ(SD) 2
0.05
0.01
0
20
‐0.62
(0.18)
10
‐0.69
(0.28)
20
‐0.63
(0.18)
10
‐0.69
(0.28)
20
‐0.62
(0.18)
10
‐0.60
(0.28)
20
‐0.64
(0.19)
10
‐0.58
(0.26)
20
‐0.59
(0.17)
10
‐0.64
(0.26)
20
‐0.60
(0.18)
10
‐0.63
(0.26)
20
‐0.54
(0.18)
10
‐0.59
(0.27)
20
‐0.58(0.19)
10
‐0.59
(0.26)
20
‐0.54
(0.19)
10
‐0.60
(0.25)
20
‐0.53
(0.17)
10
‐0.62
(0.29)
2
3
3
4
4
5
5
10
10
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.5
0
0.5
0
0.5
0
0.5
0
0.5
2
0.01
0.01
0
20
‐0.61
(0.18)
2
0.01
0.01
0.5
20
‐0.63
(0.19)
3
0.01
0.01
0
20
‐0.72
(0.19)
3
0.01
0.01
0.5
20
‐0.69
(0.19)
4
0.01
0.01
0
20
‐0.60
(0.17)
4
0.01
0.01
0.5
20
‐0.59
(0.17)
5
0.01
0.01
0
20
‐0.58
(0.18)
5
0.01
0.01
0.5
20
‐0.57
(0.20)
10
0.01
0.01
0
20
‐0.51
(0.17)
10
0.01
0.01
0.5
20
‐0.53
(0.17)
2
0.01
0.05
0
20
‐0.66
(0.18)
2
0.01
0.05
0.5
20
‐0.64
(0.18)
3
0.01
0.05
0
20
‐0.61
(0.18)
3
0.01
0.05
0.5
20
‐0.61
(0.18)
2
SI
T.
Bataillon,
T.
Zhang,
and
R.
Kassen
4
0.01
0.05
0
20
‐0.59
(0.18)
4
0.01
0.05
0.5
20
‐0.58
(0.18)
5
0.01
0.05
0
20
‐0.53
(0.18)
5
0.01
0.05
0.5
20
‐0.51
(0.19)
10
0.01
0.05
0
20
‐0.58
(0.18)
10
0.01
0.05
0.5
20
‐0.55
(0.19)
Each
dataset
consists
in
nsample
genotypes
drawn
from
the
fraction
of
the
underlying
fitness
distribution
exceeding
the
wild
type.
Fitness
of
each
genotype
is
drawn
from
a
distribution
of
fitness
values
obtained
under
the
fitness
landscape
parameterized
as
in
MARTIN
et
al
(2007)
consisting
of
m
effective
dimensions
with
distance
to
the
optimum
S0.and
mean
fitness
effect
for
a
single
mutation
E(s).
Repeated
simulations
of
data
under
a
given
landscape
model
show
that
the
mean
of
empirical
k
estimates
in
datasets
simulated
with
contamination
(λ
=
0.5)
or
in
ideal
datasets
(λ
=
0)
are
very
close.
If
anything
it
is
the
sample
size
(10
vs.
20)
that
affects
the
behavior
of
the
estimator
(as
previously
noted
by
ROKYTA
et
al
2008)
Notes:
a:Mean
fraction
of
mutant
genotypes
exceeding
the
wild
type
,estimated
from
100,000
simulated
mutants
genotypes.
b:
Empirical
mean
(and
SD)
of
the
estimate
of
the
shape
parameter
k
(estimator
of
ROKYTA
et
al
2008).
Results
reported
are
based
on
1,000
independent
samples
of
size
nsample=10
or
20
favorable
mutants.
T.
Bataillon,
T.
Zhang,
and
R.
Kassen
3
SI